Exploring 3-D shapes!

Glasses not required!

Polyhedra!

A polyhedron is a 3-dimensional, closed object whose surface is made up of polygons.

Common examples: cubes and pyramids

Are these polyhedra?

Things We Can Count

Faces – the polygons on the outside of the polyhedron.

Edges – the lines that touch polygons to each other.

Vertices – the “corners” that connect edges to other edges

Most Fun Example – Soccer Ball

32 faces (20 hexagons, 12 pentagons)

60 vertices (each connected to 2 hexagons and one pentagon)

90 edges

Our goal:

Count the number of faces, edges, and vertices on each of the following polyhedra:

Cube Triangular pyramid Square pyramid

And These Things:

What These All Share:

Try and come up with a formula that relates the numbers of edges, faces, and vertices of a certain polyhedron, and see if it works for EVERY polyhedron.

Something maybe like: E + F = ????

Euler’s Polyhedron Formula:

2 EFV